Question

How many possible 5 digit numbers can be formed with the 10 digits 0 to 9 if repetitions are not allowed and zero cannot be the first digit?

Answer 1

Number of options for the first digit = 9 (1 to 9)

Number of options for the second digit = 9

Number of options for the third digit = 8

Number of options of fourth digit = 7

Number of options for fifth digit = 6

Number of 5 digit numbers can be formed with the 10 digits 0 to 9 if repetitions are not allowed and zero cannot be the first digit = 9 x 9 x 8 x 7 x 6

= 27,216

OR

Number of options for first digit = 9

Number of digits remaining = 9

Permutations for remaining 4 digits from 9 = 9P4

= 9!/(5-4)!

= 3024

Number of 5 digit numbers can be formed with the 10 digits 0 to 9 if repetitions are not allowed and zero cannot be the first digit = 9 x 3024

= 27,216